Existence of nonoscillatory solutions of a class of nonlinear difference equations with a forced term

Bing Gen Zhang; Y. J. Sun

Mathematica Bohemica (2001)

  • Volume: 126, Issue: 3, page 639-647
  • ISSN: 0862-7959

Abstract

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In this paper, necessary and sufficient conditions for the existence of nonoscillatory solutions of the forced nonlinear difference equation Δ ( x n - p n x τ ( n ) ) + f ( n , x σ ( n ) ) = q n are obtained. Examples are included to illustrate the results.

How to cite

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Zhang, Bing Gen, and Sun, Y. J.. "Existence of nonoscillatory solutions of a class of nonlinear difference equations with a forced term." Mathematica Bohemica 126.3 (2001): 639-647. <http://eudml.org/doc/248883>.

@article{Zhang2001,
abstract = {In this paper, necessary and sufficient conditions for the existence of nonoscillatory solutions of the forced nonlinear difference equation \[ \Delta (x\_\{n\}-p\_\{n\} x\_\{\tau (n)\})+f(n,x\_\{\sigma (n)\})=q\_\{n\} \] are obtained. Examples are included to illustrate the results.},
author = {Zhang, Bing Gen, Sun, Y. J.},
journal = {Mathematica Bohemica},
keywords = {difference equations; nonlinear; forced term; nonoscillation; nonoscillatory solutions; forced nonlinear difference equation},
language = {eng},
number = {3},
pages = {639-647},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence of nonoscillatory solutions of a class of nonlinear difference equations with a forced term},
url = {http://eudml.org/doc/248883},
volume = {126},
year = {2001},
}

TY - JOUR
AU - Zhang, Bing Gen
AU - Sun, Y. J.
TI - Existence of nonoscillatory solutions of a class of nonlinear difference equations with a forced term
JO - Mathematica Bohemica
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 126
IS - 3
SP - 639
EP - 647
AB - In this paper, necessary and sufficient conditions for the existence of nonoscillatory solutions of the forced nonlinear difference equation \[ \Delta (x_{n}-p_{n} x_{\tau (n)})+f(n,x_{\sigma (n)})=q_{n} \] are obtained. Examples are included to illustrate the results.
LA - eng
KW - difference equations; nonlinear; forced term; nonoscillation; nonoscillatory solutions; forced nonlinear difference equation
UR - http://eudml.org/doc/248883
ER -

References

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  1. Difference Equations and Inequalities, Marcel Dekker, New York, 2000. (2000) Zbl0952.39001MR1740241
  2. Advanced Topics in Difference Equations, Kluwer, Dordrecht, 1997. (1997) MR1447437
  3. The existence of the bounded positive solutions of delay difference equations, PanAmerican Math. J. 3 (1993), 79–94. (1993) MR1201542
  4. On the asymptotic behavior of solutions of a nonlinear difference equation, Proceedings of the First International Conference on Difference Equations, Gordan and Breach, New York, 1995, pp. 223–229. (1995) MR1678694
  5. Oscillatory and asymptotic behavior of solutions of nonlinear neutral-type difference equations, J. Austral. Math. Soc. Ser. B 38 (1996), 163–171. (1996) MR1414357
  6. Boundedness and asymptotic behavior of solutions of a forced difference equations, Internat. J. Math. and Math. Sci. 17 (1994), 397–400. (1994) MR1261087
  7. Oscillation and nonoscillation results for nonlinear difference equations with a forcing term, Proceedings of the first International Conference on Difference Equations, Gordan and Breach, New York, 1995, pp. 213–222. (1995) MR1678690
  8. The existence of nonoscillatory and oscillatory solutions of neutral difference equations, Dynam. Systems Appl. 6 (1997), 411–428. (1997) MR1470829
  9. On existence of positive solutions and bounded oscillations for neutral difference equations, J. Math. Anal. Appl. 166 (1992), 272–287. (1992) MR1159653
  10. On the oscillation of solutions and existence of positive solutions of neutral difference equations, J. Math. Anal. Appl. 158 (1991), 213–233. (1991) MR1113411
  11. On existence of positive solutions and oscillations of neutral difference equations of odd order, J. Differ. Equations Appl. 2 (1996), 175–183. (1996) MR1384567
  12. Existence of nonoscillatory solutions of first order nonlinear neutral equations, J. Austral. Math. Soc. Ser. B 32 (1990), 180–192. (1990) Zbl0723.34069
  13. The existence of nonoscillatory and oscillatory solutions of neutral difference equations, Dynam. Systems Appl. 6 (1997), 411–428. (1997) MR1470829

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